ABB Analysis Tasks
Molly Wilson
12/5/2017
1 Data overview:
- Fish follows (2 min) conducted at sites in Antigua (6), Barbuda (3) and Bonaire (4) from March-August 2017
- Follows tracked time spent grazing, bite rates, and competitive interactions (among scarids and with damselfish)
- Follows targeted Sparisoma viride, Scarus vetula, and Sparisoma aurofrenatum of both initial and terminal phases +Sparisoma aurofrenatum were not followed in Bonaire, but added in Antigua and Bonaire due to low abundances of other two species. Some sites in Antigua and Barbuda had no/low represenation from terminal phase viride and vetula
- Site level factors (benthic, fish, and rugosity) assessed at each of the 13 sites
2 Examing variable distributions and relationships
2.1 Site-level predictor variables: fish, benthic, and rugosity
2.1.1 Distributions
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
2.1.2 Correlations
Many correlations here, both within benthic/fish categories and across categories. Rugosity is correlated with both fish and benthic variables. I will examine correlations within fish community and benthic community variables to decide which I can omit and which I will integrate through PCA. Whether I include benthic variables as predictor or response variables will determine if I need to worry about fish~benthic correlations.
Variables carn.DEN and carn.BM are essentially identical - I will remove carn.DEN and use carn.BM as the main preditor metric. Total fish biomass and density (tot.BM and tot.DEN) are highly correlated with both scarid and carnivore variables, so I will remove them. Conspecific biomass is highly correlated with scarid biomass so I will remove it as well (and should possibly also remove conspec.DEN?). The selected variables I will proceed with are as follows: 
Scarid biomass, carnivore biomass, and rugosity should be integrated via PCA. Scarid density and conspecific density should also be combined, or one should be omitted.
All benthic variables are highly correlated. I can omit cover_CCA and cover_MA (accounted for by canopy_MA). The rest should be combined via PCA. First I will assess remaining correlations between selected benthic and fish community variables:
Unsure how to proceed here if I do end up using both benthic and fish community variables as predictors, because some are corellated (esp. scarid.BM.s and all benthic variables….). It looks like I would integrate scar.BM and carn.BM into a PCA with all other benthic/rugosity variables. Variables scar.DEN and conspec.DEN are relatively independent of all other variables (except each other).
Current outline for site-level PCA tasks: If benthic=predictor: - cover_LC + cover_TA + canopy_MA + canopy_TA + rugosity + scar.BM + carn.BM - scar.DEN + conspec.DEN If benthic=response: - rugosity + scar.BM + carn.BM - cover_LC + cover_TA + canopy_MA + canopy_TA - scar.DEN + conspec.DEN
2.2 Fish-level response variables: grazing behaviors
2.2.1 Distributions
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
2.2.2 Corellations
Variable for.bites is correlated with nearly all other variables, so will be omitted. Variables g.farc, FR. and for.dur are still correlated and should be assessed with a PCA. Variable BR can be a standalone variable.
Grazing PCA: - g.frac + FR + for.dur - (BR as standalone)
3 Exploratory bivariate plots
3.1 Grazing as a function of fish length
3.2 Grazing as a function of scarid biomass and density
anubon <- data %>% filter(Island!="Barbuda")
ggplot(anubon,aes(x=scar.BM,y=FR))+facet_grid(.~Species)+geom_smooth(method="loess")+geom_point(shape=18)+ggtitle("Feeding rate by scarid biomass") + theme_minimal() +labs(y="Feeding rate (bites/hr)",x="Scarid Biomass (g/100m2)") + theme(plot.title = element_text(hjust = 0.5))
3.3 Competitive interactions
4 PCAs
Do I need to normalize my variables pre-PCA? Currently just scaled, except for grazing response variables which are log-transformed
4.1 Predictors
4.1.1 All predictors
predictors <- site.sum %>% select(cover_LC,cover_TA,canopy_MA,canopy_TA,rugosity,scar.BM,scar.DEN,carn.BM) # should it matter if I use site level summary data vs. full follow dataset (where site-level data has been joined?)
pca <- prcomp(na.omit(predictors),center = TRUE,scale. = TRUE)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 2.1310 1.4982 0.79477 0.47902 0.45634 0.30914
## Proportion of Variance 0.5677 0.2806 0.07896 0.02868 0.02603 0.01195
## Cumulative Proportion 0.5677 0.8482 0.92719 0.95587 0.98190 0.99385
## PC7 PC8
## Standard deviation 0.21046 0.07020
## Proportion of Variance 0.00554 0.00062
## Cumulative Proportion 0.99938 1.00000plot(pca,type="l")
ggbiplot(pca, obs.scale = 1, var.scale = 1, groups=site.sum$Island, ellipse = TRUE, circle = TRUE, varname.size = 2) + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal()
### Benthic variables
predictors1 <- site.sum %>% select(cover_LC,cover_TA,canopy_MA,canopy_TA,rugosity) # should it matter if I use site level summary data vs. full follow dataset (where site-level data has been joined?)
pca1 <- prcomp(na.omit(predictors1),center = TRUE,scale. = TRUE)
summary(pca1)## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Standard deviation 1.7912 1.1130 0.60454 0.33002 0.27993
## Proportion of Variance 0.6417 0.2478 0.07309 0.02178 0.01567
## Cumulative Proportion 0.6417 0.8894 0.96255 0.98433 1.00000plot(pca1,type="l")
ggbiplot(pca1, obs.scale = 1, var.scale = 1, groups=site.sum$Island, ellipse = TRUE, circle = TRUE, loadings.label.repel=TRUE) + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal()
# add PC1 and PC2 as variables in dataset
pca1.scores <- as.data.frame(pca1$x) %>% select(PC1,PC2)
site.sum <- site.sum %>% bind_cols(pca1.scores)
pca1.scores <- select(site.sum,Site,PC1,PC2)
data <- data %>% left_join(pca1.scores,by="Site")4.1.2 Fish community variables
predictors2 <- site.sum %>% select(scar.BM,scar.DEN,carn.BM) # should it matter if I use site level summary data vs. full follow dataset (where site-level data has been joined?)
pca2 <- prcomp(na.omit(predictors2),center = TRUE,scale. = TRUE)
summary(pca2)## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.4140 0.9480 0.31926
## Proportion of Variance 0.6665 0.2996 0.03398
## Cumulative Proportion 0.6665 0.9660 1.00000plot(pca2,type="l")
ggbiplot(pca2, obs.scale = 1, var.scale = 1, groups=site.sum$Island, ellipse = TRUE, circle = TRUE, loadings.label.repel=TRUE) + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal()
4.2 Response variables
4.2.1 Grazing behaviors
log transform increases P1 explained variance here… Currently for.dur has several NA values (for individuals that didn’t graze)… I am omitting that variable for now because I don’t want to omit non-grazing individuals (instead would like to keep them as grazing=0
response <- data %>% select(g.frac,TDB,BR)
log.vars5 <- log(response[,1:3])
pca3 <- prcomp(na.omit(response),center = TRUE,scale. = TRUE)
summary(pca3)## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.3412 1.0296 0.37576
## Proportion of Variance 0.5996 0.3534 0.04707
## Cumulative Proportion 0.5996 0.9529 1.00000plot(pca3,type="l")
ggbiplot(pca3, obs.scale = 1, var.scale = 1, groups=data$Island,shape=data$Island,ellipse = TRUE, circle = TRUE, alpha=0.8,varname.size = 5) + theme_minimal() + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + labs(title="Grazing behaviors by island") + theme(plot.title = element_text(hjust = 0.5))
response <- data %>% select(g.frac,FR,BR)
log.vars5 <- log(response[,1:3])
pca3 <- prcomp(na.omit(response),center = TRUE,scale. = TRUE)
summary(pca3)## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.3412 1.0296 0.37576
## Proportion of Variance 0.5996 0.3534 0.04707
## Cumulative Proportion 0.5996 0.9529 1.00000plot(pca3,type="l")
ggbiplot(pca3, obs.scale = 1, var.scale = 1,ellipse = TRUE, circle = TRUE, alpha=0.4,varname.size = 5) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal() +geom_point(aes(col=data$scar.BM)) + labs(col="Scarid Biomass (g/100m2)", title="Grazing Behaviors by Scarid Biomass") + theme(plot.title = element_text(hjust = 0.5))
5 Model trials: all species compiled
5.1 Basic lm to assess predictors of interest
-site-level predictors: scar.BM,scar.DEN,carn.BM,benthic (PC1,PC2) -fish-level predictors: species, phase, length –eventually run separately for different species –species*scar.BM interaction? -random effects: island -response variables: g.frac, BR (?), and FR (run separately)
5.1.1 Feeding rates
initial<-data%>%filter(Phase=="i") # for analysis with initial only
lm_FR <- lm(FR~scar.BM*Species+carn.BM+Length.cm+PC1+PC2, data=data)
summary(lm_FR)##
## Call:
## lm(formula = FR ~ scar.BM * Species + carn.BM + Length.cm + PC1 +
## PC2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1387.47 -225.33 -4.04 204.63 2248.37
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 1211.83909 80.23415 15.104
## scar.BM 0.16506 0.03162 5.220
## SpeciesSparisoma aurofrenatum -327.32658 85.52936 -3.827
## SpeciesSparisoma viride -287.65128 64.61926 -4.451
## carn.BM -0.20771 0.04036 -5.146
## Length.cm -16.50830 2.34232 -7.048
## PC1 -151.35094 13.89933 -10.889
## PC2 76.96201 17.45963 4.408
## scar.BM:SpeciesSparisoma aurofrenatum -0.06957 0.06376 -1.091
## scar.BM:SpeciesSparisoma viride -0.12717 0.02216 -5.738
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## scar.BM 2.30e-07 ***
## SpeciesSparisoma aurofrenatum 0.00014 ***
## SpeciesSparisoma viride 9.77e-06 ***
## carn.BM 3.38e-07 ***
## Length.cm 4.01e-12 ***
## PC1 < 2e-16 ***
## PC2 1.19e-05 ***
## scar.BM:SpeciesSparisoma aurofrenatum 0.27559
## scar.BM:SpeciesSparisoma viride 1.37e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 403.8 on 778 degrees of freedom
## (7 observations deleted due to missingness)
## Multiple R-squared: 0.5151, Adjusted R-squared: 0.5095
## F-statistic: 91.81 on 9 and 778 DF, p-value: < 2.2e-16#vif(lm_FR)Notes: nearly everything is significant? Significant interaction between scar.BM and species for Spar. viride. carn.BM and scar.BM are highly positively correlated (~0.86) - is it ok to include both? R2 goes up slightly with initial only
5.1.2 Fraction of time grazing
lm_g.frac <- lm(g.frac~Species*scar.BM+scar.DEN+carn.BM+Phase+Length.cm+PC1+PC2, data=data)
summary(lm_g.frac)##
## Call:
## lm(formula = g.frac ~ Species * scar.BM + scar.DEN + carn.BM +
## Phase + Length.cm + PC1 + PC2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49041 -0.14465 -0.01811 0.12947 0.74660
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 3.776e-01 5.334e-02 7.079
## SpeciesSparisoma aurofrenatum 5.710e-02 4.556e-02 1.253
## SpeciesSparisoma viride 6.663e-02 3.349e-02 1.989
## scar.BM 5.288e-05 1.793e-05 2.949
## scar.DEN 2.928e-04 8.293e-04 0.353
## carn.BM -8.772e-05 2.227e-05 -3.939
## Phaset -5.956e-02 1.995e-02 -2.985
## Length.cm -3.462e-03 1.540e-03 -2.249
## PC1 -7.058e-02 7.627e-03 -9.255
## PC2 2.719e-02 2.165e-02 1.256
## SpeciesSparisoma aurofrenatum:scar.BM -4.259e-05 3.351e-05 -1.271
## SpeciesSparisoma viride:scar.BM -2.506e-05 1.149e-05 -2.182
## Pr(>|t|)
## (Intercept) 3.25e-12 ***
## SpeciesSparisoma aurofrenatum 0.21053
## SpeciesSparisoma viride 0.04701 *
## scar.BM 0.00329 **
## scar.DEN 0.72412
## carn.BM 8.93e-05 ***
## Phaset 0.00292 **
## Length.cm 0.02482 *
## PC1 < 2e-16 ***
## PC2 0.20963
## SpeciesSparisoma aurofrenatum:scar.BM 0.20408
## SpeciesSparisoma viride:scar.BM 0.02944 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2092 on 776 degrees of freedom
## (7 observations deleted due to missingness)
## Multiple R-squared: 0.2522, Adjusted R-squared: 0.2416
## F-statistic: 23.79 on 11 and 776 DF, p-value: < 2.2e-16Notes: carn.BM and PC1 are strongest predictors of time spent grazing, scar.BM and phase are also significant. Slight significance of species, length, and species-scar.BM interaction
5.2 Mixed effects models
- random effect: island
5.2.1 Feeding rates
lme_FR <- lme(FR~Phase+Length.cm+Species*scar.BM+scar.DEN+carn.BM+PC1+PC2,data=data,random=~1|Island, na.action = na.omit)
summary(lme_FR)## Linear mixed-effects model fit by REML
## Data: data
## AIC BIC logLik
## 11666.93 11732.08 -5819.463
##
## Random effects:
## Formula: ~1 | Island
## (Intercept) Residual
## StdDev: 0.1453803 401.3498
##
## Fixed effects: FR ~ Phase + Length.cm + Species * scar.BM + scar.DEN + carn.BM + PC1 + PC2
## Value Std.Error DF t-value
## (Intercept) 1134.8645 102.35027 774 11.088046
## Phaset -128.6993 38.28480 774 -3.361629
## Length.cm -10.3978 2.95378 774 -3.520178
## SpeciesSparisoma aurofrenatum -267.4282 87.41905 774 -3.059153
## SpeciesSparisoma viride -280.6170 64.25914 774 -4.366958
## scar.BM 0.1420 0.03441 774 4.128253
## scar.DEN -1.1438 1.59105 774 -0.718880
## carn.BM -0.1760 0.04273 774 -4.119365
## PC1 -154.4344 14.63337 774 -10.553571
## PC2 39.5248 41.54261 774 0.951427
## SpeciesSparisoma aurofrenatum:scar.BM -0.0829 0.06429 774 -1.289275
## SpeciesSparisoma viride:scar.BM -0.1279 0.02204 774 -5.805561
## p-value
## (Intercept) 0.0000
## Phaset 0.0008
## Length.cm 0.0005
## SpeciesSparisoma aurofrenatum 0.0023
## SpeciesSparisoma viride 0.0000
## scar.BM 0.0000
## scar.DEN 0.4724
## carn.BM 0.0000
## PC1 0.0000
## PC2 0.3417
## SpeciesSparisoma aurofrenatum:scar.BM 0.1977
## SpeciesSparisoma viride:scar.BM 0.0000
## Correlation:
## (Intr) Phaset Lngth. SpcsSa SpcsSv
## Phaset 0.315
## Length.cm -0.647 -0.616
## SpeciesSparisoma aurofrenatum -0.375 -0.178 0.229
## SpeciesSparisoma viride -0.428 -0.033 0.055 0.490
## scar.BM -0.450 0.134 -0.158 0.296 0.367
## scar.DEN -0.527 0.045 -0.027 -0.158 0.002
## carn.BM 0.173 -0.170 0.150 -0.095 -0.073
## PC1 -0.360 0.007 0.070 -0.032 -0.081
## PC2 -0.423 0.116 -0.117 -0.182 0.019
## SpeciesSparisoma aurofrenatum:scar.BM 0.093 0.034 -0.026 -0.787 -0.181
## SpeciesSparisoma viride:scar.BM 0.374 0.015 -0.025 -0.413 -0.858
## scr.BM sc.DEN crn.BM PC1 PC2
## Phaset
## Length.cm
## SpeciesSparisoma aurofrenatum
## SpeciesSparisoma viride
## scar.BM
## scar.DEN 0.390
## carn.BM -0.770 -0.307
## PC1 0.466 0.330 -0.113
## PC2 0.450 0.905 -0.461 0.246
## SpeciesSparisoma aurofrenatum:scar.BM -0.263 0.167 0.101 -0.150 0.219
## SpeciesSparisoma viride:scar.BM -0.414 -0.025 0.042 0.012 -0.027
## SSa:.B
## Phaset
## Length.cm
## SpeciesSparisoma aurofrenatum
## SpeciesSparisoma viride
## scar.BM
## scar.DEN
## carn.BM
## PC1
## PC2
## SpeciesSparisoma aurofrenatum:scar.BM
## SpeciesSparisoma viride:scar.BM 0.207
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.53931587 -0.55545351 -0.04258537 0.53462153 5.58730104
##
## Number of Observations: 788
## Number of Groups: 3Notes: nearly everything is significant except for PC2 and scar.DEN?
5.2.2 Fraction of time spent grazing
lme_g.frac <- lme(g.frac~Phase+Length.cm+Species*scar.BM+scar.DEN+carn.BM+PC1+PC2,data=data,random=~1|Island, na.action = na.omit)
summary(lme_g.frac)## Linear mixed-effects model fit by REML
## Data: data
## AIC BIC logLik
## -65.88562 -0.727487 46.94281
##
## Random effects:
## Formula: ~1 | Island
## (Intercept) Residual
## StdDev: 0.07537797 0.2088254
##
## Fixed effects: g.frac ~ Phase + Length.cm + Species * scar.BM + scar.DEN + carn.BM + PC1 + PC2
## Value Std.Error DF t-value
## (Intercept) 0.4111687 0.07424279 774 5.538163
## Phaset -0.0606669 0.02011154 774 -3.016522
## Length.cm -0.0033187 0.00155022 774 -2.140818
## SpeciesSparisoma aurofrenatum 0.0474800 0.04591200 774 1.034151
## SpeciesSparisoma viride 0.0639031 0.03347915 774 1.908742
## scar.BM 0.0000415 0.00001926 774 2.155762
## scar.DEN -0.0002628 0.00117601 774 -0.223444
## carn.BM -0.0000761 0.00002335 774 -3.258104
## PC1 -0.0451251 0.01798320 774 -2.509291
## PC2 0.0246092 0.02192286 774 1.122536
## SpeciesSparisoma aurofrenatum:scar.BM -0.0000328 0.00003400 774 -0.965756
## SpeciesSparisoma viride:scar.BM -0.0000242 0.00001148 774 -2.107265
## p-value
## (Intercept) 0.0000
## Phaset 0.0026
## Length.cm 0.0326
## SpeciesSparisoma aurofrenatum 0.3014
## SpeciesSparisoma viride 0.0567
## scar.BM 0.0314
## scar.DEN 0.8232
## carn.BM 0.0012
## PC1 0.0123
## PC2 0.2620
## SpeciesSparisoma aurofrenatum:scar.BM 0.3345
## SpeciesSparisoma viride:scar.BM 0.0354
## Correlation:
## (Intr) Phaset Lngth. SpcsSa SpcsSv
## Phaset 0.180
## Length.cm -0.414 -0.622
## SpeciesSparisoma aurofrenatum -0.291 -0.177 0.223
## SpeciesSparisoma viride -0.317 -0.033 0.053 0.491
## scar.BM -0.381 0.126 -0.157 0.323 0.359
## scar.DEN -0.512 0.128 -0.112 -0.102 0.008
## carn.BM 0.204 -0.171 0.160 -0.129 -0.084
## PC1 0.067 0.008 0.048 -0.136 -0.081
## PC2 -0.357 0.136 -0.136 -0.175 0.020
## SpeciesSparisoma aurofrenatum:scar.BM 0.108 0.030 -0.019 -0.791 -0.187
## SpeciesSparisoma viride:scar.BM 0.276 0.016 -0.024 -0.415 -0.859
## scr.BM sc.DEN crn.BM PC1 PC2
## Phaset
## Length.cm
## SpeciesSparisoma aurofrenatum
## SpeciesSparisoma viride
## scar.BM
## scar.DEN 0.312
## carn.BM -0.791 -0.298
## PC1 -0.150 0.012 0.219
## PC2 0.427 0.747 -0.455 0.078
## SpeciesSparisoma aurofrenatum:scar.BM -0.307 0.081 0.148 0.098 0.204
## SpeciesSparisoma viride:scar.BM -0.402 -0.018 0.054 0.050 -0.027
## SSa:.B
## Phaset
## Length.cm
## SpeciesSparisoma aurofrenatum
## SpeciesSparisoma viride
## scar.BM
## scar.DEN
## carn.BM
## PC1
## PC2
## SpeciesSparisoma aurofrenatum:scar.BM
## SpeciesSparisoma viride:scar.BM 0.213
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.38961997 -0.68622025 -0.08236243 0.61547559 3.60169508
##
## Number of Observations: 788
## Number of Groups: 3Notes: carn.BM and phase are strongest predictors, followed by scar.BM, PC1, and length. Also significant interaction between
6 Model trials: species run individually
stop<-data%>%filter(Species.Code=="stop")
qup<-data%>%filter(Species.Code=="qup")
rbp<-data%>%filter(Species.Code=="rbp")6.1 Feeding rates
lme_FR_stop <- lme(FR~Phase+Length.cm+scar.BM+scar.DEN+carn.BM+PC1+PC2,data=stop,random=~1|Island, na.action = na.omit)
summary(lme_FR_stop)## Linear mixed-effects model fit by REML
## Data: stop
## AIC BIC logLik
## 4718.924 4756.915 -2349.462
##
## Random effects:
## Formula: ~1 | Island
## (Intercept) Residual
## StdDev: 196.3731 264.1006
##
## Fixed effects: FR ~ Phase + Length.cm + scar.BM + scar.DEN + carn.BM + PC1 + PC2
## Value Std.Error DF t-value p-value
## (Intercept) 647.6314 155.50536 328 4.164689 0.0000
## Phaset -59.7705 37.76582 328 -1.582662 0.1145
## Length.cm -6.7368 2.88840 328 -2.332367 0.0203
## scar.BM 0.0463 0.03433 328 1.347536 0.1787
## scar.DEN 0.1381 2.40977 328 0.057325 0.9543
## carn.BM -0.1121 0.04531 328 -2.474794 0.0138
## PC1 -22.1444 39.81757 328 -0.556147 0.5785
## PC2 66.5859 43.94301 328 1.515278 0.1307
## Correlation:
## (Intr) Phaset Lngth. scr.BM sc.DEN crn.BM PC1
## Phaset 0.131
## Length.cm -0.325 -0.585
## scar.BM -0.254 0.177 -0.259
## scar.DEN -0.506 0.100 -0.119 0.365
## carn.BM 0.175 -0.216 0.230 -0.869 -0.339
## PC1 0.050 -0.046 0.108 -0.226 -0.030 0.293
## PC2 -0.362 0.122 -0.149 0.545 0.750 -0.532 0.022
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.34182299 -0.68334527 -0.02454934 0.63818887 2.43642991
##
## Number of Observations: 338
## Number of Groups: 3Notes: carn.BM and length are signifigant predictors
lme_FR_qup <- lme(FR~Phase+Length.cm+scar.BM+scar.DEN+carn.BM+PC1+PC2,data=qup,random=~1|Island, na.action = na.omit)
summary(lme_FR_qup)## Linear mixed-effects model fit by REML
## Data: qup
## AIC BIC logLik
## 4371.329 4407.569 -2175.665
##
## Random effects:
## Formula: ~1 | Island
## (Intercept) Residual
## StdDev: 213.1221 541.4963
##
## Fixed effects: FR ~ Phase + Length.cm + scar.BM + scar.DEN + carn.BM + PC1 + PC2
## Value Std.Error DF t-value p-value
## (Intercept) 1569.8146 290.22840 275 5.408894 0.0000
## Phaset -358.1420 99.66307 275 -3.593528 0.0004
## Length.cm -7.6700 6.50751 275 -1.178637 0.2396
## scar.BM 0.0785 0.07296 275 1.076240 0.2828
## scar.DEN -12.2987 5.61631 275 -2.189824 0.0294
## carn.BM -0.2373 0.09823 275 -2.416166 0.0163
## PC1 -253.0035 62.14704 275 -4.071047 0.0001
## PC2 24.6422 92.05672 275 0.267685 0.7891
## Correlation:
## (Intr) Phaset Lngth. scr.BM sc.DEN crn.BM PC1
## Phaset 0.272
## Length.cm -0.489 -0.731
## scar.BM -0.473 0.080 -0.070
## scar.DEN -0.682 0.092 -0.035 0.461
## carn.BM 0.342 -0.103 0.072 -0.865 -0.402
## PC1 0.057 0.035 -0.004 -0.186 0.033 0.284
## PC2 -0.463 0.121 -0.113 0.540 0.738 -0.557 -0.041
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.51677111 -0.68751588 -0.05135616 0.66825882 3.88093297
##
## Number of Observations: 285
## Number of Groups: 3Notes: PC1 is strongest (magnitude) predictors. Also significant are phase, carn.BM and scar.DEN
lme_FR_rbp <- lme(FR~Phase+Length.cm+scar.BM+scar.DEN+carn.BM+PC1+PC2,data=rbp,random=~1|Island, na.action = na.omit)
summary(lme_FR_rbp)## Linear mixed-effects model fit by REML
## Data: rbp
## AIC BIC logLik
## 2196.698 2227.26 -1088.349
##
## Random effects:
## Formula: ~1 | Island
## (Intercept) Residual
## StdDev: 0.08717848 200.7262
##
## Fixed effects: FR ~ Phase + Length.cm + scar.BM + scar.DEN + carn.BM + PC1 + PC2
## Value Std.Error DF t-value p-value
## (Intercept) 536.2508 199.55836 156 2.6871877 0.0080
## Phaset -15.3253 39.54521 156 -0.3875383 0.6989
## Length.cm -14.7100 6.34149 156 -2.3196497 0.0217
## scar.BM 0.0675 0.04749 156 1.4219603 0.1570
## scar.DEN 3.9166 2.75859 156 1.4197947 0.1577
## carn.BM 0.0471 0.10945 156 0.4302947 0.6676
## PC1 -46.2121 40.49602 156 -1.1411516 0.2556
## PC2 116.4946 64.49851 156 1.8061599 0.0728
## Correlation:
## (Intr) Phaset Lngth. scr.BM sc.DEN crn.BM PC1
## Phaset 0.187
## Length.cm -0.646 -0.509
## scar.BM -0.414 0.226 -0.152
## scar.DEN -0.770 0.051 0.068 0.589
## carn.BM -0.419 -0.214 0.148 -0.107 0.465
## PC1 -0.451 0.180 0.108 0.269 0.370 -0.260
## PC2 -0.687 0.091 0.008 0.691 0.955 0.369 0.247
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.3215647 -0.5678367 -0.1688058 0.5817523 3.7193249
##
## Number of Observations: 165
## Number of Groups: 26.2 Notes: much more variable, less predictable. Maybe take out of overall analysis?
To Do as of Nov. 7 * incorporate PCs * boosted regression trees ecosphere 2017 adrians paper * simpler graphs with just herb density x axis - grazing behaviors y, facet by species * Speciesdensity as fixed effect~~ Species as random effect *break out species and run separately~~